The slash thing appears in two forms in Fletcher's notes: color on red, and red on color. Lamentably, that's not quite systematically applied in practice, as none of the Academy scenes feature the supposed "instructor" model, red on color. Dropping the concept and accepting full red as a generic Academy color applicable to instructors as well would basically eliminate some discrepancies, such as Valeris.

Let's not try to use the reboot as an argument for the original canon, shall we?

I'm curious as to what the next movie in the reboot series has to offer in the uniform, rank, and training department; so far, things don't seem to be too contradictory...

But even dismissing STXI, the backstory of ST2 has Kirk do the no-win scenario and thus supposedly complete his Command studies while a "Cadet", as per McCoy's words. Makes sense, I guess: driven individuals won't wait until after graduation. Saavik may have dedicated the precious study hours to some sciences pursuit or another, calculating that she could get the command training later on; the Academy certainly appears flexible that way, in both universes.

Now that is simply not true - otherwise Kirk and co. would be department-hopping every other week.

If we don't count onscreen hours but rather individual costuming decisions, it's not really exaggerated to say that more (main and guest) characters in TOS are introduced in "wrong" colors or ranks than in "right" ones. When they then stick to those, wrong simply becomes right.

Are you going to do the same contortions in order to excuse all of their little flubs?

Basically, I'm saying that none of the complex models created backstage are valid, and that the simple thing is to assume Starfleet in-universe uses a complex (or flexible) model that differs from the defunct intended ones. The little flubs are features rather than bugs: some science officers really wear red in TOS for some unknown but perfectly valid reason, and the "single excuse" that this just happens and should happen is better than the "double excuse" that this was an error motivated by this complex out-universe factor or other (the character looked better in that color, there were no sizes available that week for the other color, whatnot).

Versus assuming that either at least some of those enlisted crewmembers were there because they were, in fact, fully qualified and did operate those positions; or because the regular bridge crew were already injured/dead/dying?

The former seems unlikely, considering how officer-heavy all the TOS movie era bridges are under this particular uniform scheme, and how TNG goes all-officer with the next uniform scheme again.

The latter is a perfectly okay explanation. Still, those officers apparently weren't killed by exploding consoles, as the consoles are intact - begging the question of what killed or incapacitated them; did all perhaps stand beneath one of those collapsing girders? Or would this lend support to the model of a large, round bridge, where officers at forward stations were lost when half the bridge was destroyed? We could even speculate that the bridge lost life support at some point when Garrett was elsewhere (scrambing up from her quarters in the early stages of the fight?), killing everybody on the bridge, and life support was subsequently restored and the bridge crewed by the personnel we see.

But Fletcher's scheme already crumbles under the weight of errors elsewhere, so it should not be considered as a strict limiting factor when considering our options here, either.